https://file.aiquickdraw.com/mathbot/file/1726738603083o0hfwto5.jpg

The problem states that in the figure, \( B \) is between \( A \) and \( C \), and \( C \) is between \( B \) and \( D \). Given the following lengths:

- \( AC = 10 \)
- \( BD = 9 \)
- \( BC = 7 \)

We are tasked with finding \( AD \).

### Solution:

1. Start by noting that \( AC = AB + BC \). Since \( B \) is between \( A \) and \( C \), we can find \( AB \) by subtracting:
   \[
   AB = AC - BC = 10 - 7 = 3
   \]

2. Next, \( AD \) is the total distance from \( A \) to \( D \), which can be broken down as \( AD = AB + BD \). Substituting the values:
   \[
   AD = AB + BD = 3 + 9 = 12
   \]

Thus, the length of \( AD \) is \( \boxed{12} \).

Let me know if you'd like further details!

Here are some related questions:
1. How would the calculation change if \( B \) was not between \( A \) and \( C \)?
2. What if \( AC \) and \( BD \) were given as variables instead of specific numbers?
3. How can this concept be extended to three-dimensional geometry?
4. What if \( C \) were not between \( B \) and \( D \), how would that affect \( AD \)?
5. How can you represent this problem using algebraic expressions?

**Tip:** Always check the relationships between the points (e.g., which point is between others) carefully before solving such geometry problems.

In the figure below, B is between A and C, and C is between B and D. If AC = 10, BD = 9, and BC = 7, find AD.

Learn how to find the length of AD when given AC = 10, BD = 9, and BC = 7. This problem involves basic geometry concepts, focusing on linear segments. Suitable for students in Grades 6-8.

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